if the tangent at the point p on the circle x^2+y^2+6x+6y=2 meet the line 5x-2y+6=0 at a point q on y axis then pq=

Dear Student,
Please find below the solution to the asked query:

S:x2+y2+6x+6y=2S:x2+y2+6x+6y-2=0Now5x-2y+6=0 meets y-axis where x=00-2y+6=02y=6y=3Qx1,y1=0,3We know that length of tangent from external point x1,y1 to circle S is S1PQ=S1=02+32+6×0+6×3-2=9+18-2=25PQ=5 Answer

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